Given that E is the midpoint of AD and BC, which of the following proves that AB∥CD?
HELP ASAP!
Answers
The proof that shows that AB∥CD in the diagram given is:
1. E is the midpoint of AD --> Given
2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint
3. E is the midpoint of BC --> Given
4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint
5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem
6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem
7. AB∥CD ---> CPCTC Theorem.
The given figure showing ΔABE ≅ ΔDCE is in the image attached below.
We know that:
E is the midpoint of AD. Therefore, AE ≅ ED by the definition of midpoint.
E is the midpoint of BC. Therefore, BE ≅ EC by the definition of midpoint.
∠AEB and ∠CED are vertical angles, therefore, ∠AEB ≅ ∠CED by the vertical angles theorem.
This means that ΔAEB and ΔDEC have:
two pairs of congruent sides - AE ≅ ED and BE ≅ EC
one pair of congruent included side - ∠AEB ≅ ∠CED
Hence, ΔABE ≅ ΔDCE by the SAS Congruence Theorem.
If both triangles are congruent, it implies that all corresponding sides and angles of ΔAEB will be congruent to that of ΔDEC.
Therefore, AB∥CD by the CPCTC Theorem.
Thus, the proof that shows that AB∥CD in the diagram given is:
1. E is the midpoint of AD --> Given
2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint
3. E is the midpoint of BC --> Given
4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint
5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem
6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem
7. AB∥CD ---> CPCTC Theorem.
Learn more about the CPCTC Theorem on:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Answers
Answer:
NoShutterStock gives the correct value: 55 miles/hr (mph)
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[] The positive interval is where the function is above the x-axis, and the negative interval is where the function is below the x-axis.
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() See attached
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Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
PLSSSSS HELP MEEEEEE DUE TODAY!!!!!
Answers
Answer:
4/5 or .8
Step-by-step explanation:
Emilino needs to arrange chairs for a drama club
meeting at his school. There are 30 students coming.
What
are the different ways he can arrange the chairs so that each
row has the same number of chairs?
This is the same as saying "find the factors of 30". There
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Answers
Answer:
(1 row & 30 columns) (2 rows & 15 columns) (3 rows & 10 columns) (5 rows & 6 columns) (6 rows & 5 columns)
Step-by-step explanation:
1 * 30 = 30
2 * 15 = 30
3 * 10 = 30
5 * 6 = 30
6 * 5 = 30